diff --git a/crates/eps/src/import/data/ops.rs b/crates/eps/src/import/data/ops.rs
index 1b78901b4..4397a0e23 100644
--- a/crates/eps/src/import/data/ops.rs
+++ b/crates/eps/src/import/data/ops.rs
@@ -401,6 +401,30 @@ impl Interp<'_> {
         Ok(())
     }
 
+    /// Skip the data an image left out (too large to read) would read from the program's own
+    /// file, so the program doesn't go on to read that data as PostScript. The filters that find
+    /// their own end without decompressing (`ASCIIHexDecode`, `ASCII85Decode`, `SubFileDecode`)
+    /// read the file up to it, the way the image reading all its data would leave it; the
+    /// filters over them, which would only decode what those pass, aren't run. When the first
+    /// filter decompresses, it is run alone, and a failure (data too large to hold) leaves the
+    /// data where it was, as before.
+    fn skip_data(&mut self, src: &Source) {
+        let Source::File(f) = src else { return };
+        let (chain, from) = match &*f.borrow() {
+            Stream::Pending { chain, from } => (chain.clone(), from.clone()),
+            _ => return,
+        };
+        let delimited = chain.iter().take_while(|c| matches!(&*c.name, "ASCIIHexDecode" | "ASCII85Decode" | "SubFileDecode")).count();
+        let head = chain.get(..delimited.max(1)).unwrap_or_default().to_vec();
+        *f.borrow_mut() = Stream::Pending { chain: head, from: from.clone() };
+        // A failure leaves the file as it was; the import goes on without the image either way.
+        if self.materialize(f).is_err() {
+            *f.borrow_mut() = Stream::Pending { chain, from };
+            return;
+        }
+        *f.borrow_mut() = Stream::Buf { data: vec![], pos: 0, rgb: None };
+    }
+
     /// The bytes a data procedure gives, called until it gives an empty string or `n` bytes.
     fn gather(&mut self, p: &Obj, n: usize) -> Res<Vec<u8>> {
         Ok(self.read_sources(&[Source::Proc(p.clone())], n, n)?.pop().unwrap_or_default())
@@ -520,6 +544,9 @@ impl Interp<'_> {
         let n = image.space.n();
         if image.w.saturating_mul(image.h) > MAX_PIXELS || stencil.w.saturating_mul(stencil.h) > MAX_PIXELS {
             self.out.warn(TOO_LARGE);
+            for src in image.sources.iter().chain(&stencil.sources) {
+                self.skip_data(src);
+            }
             return Ok(None);
         }
         if interleave != 3.0 {
@@ -626,6 +653,9 @@ impl Interp<'_> {
         }
         if s.w.saturating_mul(s.h) > MAX_PIXELS {
             self.out.warn(TOO_LARGE);
+            for src in &s.sources {
+                self.skip_data(src);
+            }
             return Ok(None);
         }
         self.alloc(s.w * s.h * 4)?;
diff --git a/crates/eps/src/import/tests_images.rs b/crates/eps/src/import/tests_images.rs
index 160074230..8aad47fc7 100644
--- a/crates/eps/src/import/tests_images.rs
+++ b/crates/eps/src/import/tests_images.rs
@@ -516,3 +516,35 @@ fn tiff_predicted_rows_at_every_depth() {
     }
     assert!(wrong.is_empty(), "{wrong:#?}");
 }
+
+/// An image too large to read is left out, and its data is skipped, as reading it would leave
+/// the program: the art after it is read, not the data as PostScript. Here the data ends at its
+/// `~>` (an inline image of a content stream run as a file, as PDF-reading prologs write it), at
+/// a `SubFileDecode` end string, and at the end of compressed data that is read whole.
+#[test]
+fn the_data_of_an_image_too_large_to_read_is_skipped() {
+    let after = "0 0 1 setrgbcolor 10 10 80 80 rectfill";
+    for program in [
+        format!(
+            "/ID {{ << /ImageType 1 /Width 10000 /Height 10000 /BitsPerComponent 8 /Decode [0 1 0 1 0 1] /ImageMatrix [1 0 0 1 0 0] \
+             /DataSource currentfile 0 (~>) /SubFileDecode filter /ASCII85Decode filter /LZWDecode filter >> \
+             /DeviceRGB setcolorspace image }} def\n\
+             currentfile 0 (endstream) /SubFileDecode filter cvx exec\nID\nJ1_V7fG\"r'\"b]2#:hXAd)~>\n{after}\nendstream\n"
+        ),
+        format!("10000 10000 8 [1 0 0 1 0 0] currentfile /ASCIIHexDecode filter false 3 colorimage\n0a1b 2c3d 4e5f>\n{after}"),
+        format!(
+            "10000 10000 8 [1 0 0 1 0 0] currentfile 0 (%%EndData) /SubFileDecode filter /FlateDecode filter image\n\
+             x\u{9c}garbage\n%%EndData\n{after}"
+        ),
+        format!(
+            "10000 10000 true [1 0 0 1 0 0] currentfile /ASCII85Decode filter imagemask\n{}\n{after}",
+            crate::ps::ascii85(&crate::ps::deflate(&[0u8; 64]))
+        ),
+    ] {
+        let r = read(&program);
+        assert!(r.warnings.iter().any(|w| w.contains("too large to read")), "{program}: {:?}", r.warnings);
+        let o = super::tests::objects(&r.document);
+        assert_eq!(o.len(), 1, "{program}: {:?}", r.warnings);
+        assert_eq!(super::tests::fill(&o[0]), Some(&vectorcraft_color::Paint::solid(vectorcraft_color::Color::rgb(0.0, 0.0, 1.0))), "{program}");
+    }
+}